SOLUTION: Determine if each function is even, odd or neither. A. F(x) = (x)^(1/3) + |x|^2 B. G(x) = (1/x) - (x)^(1/4) C. H(x) = [(x)^(1/2) + 12x]/(x^3 - 9) D. S(x) = (x^

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Question 1208085: Determine if each function is even, odd or neither.

A. F(x) = (x)^(1/3) + |x|^2

B. G(x) = (1/x) - (x)^(1/4)

C. H(x) = [(x)^(1/2) + 12x]/(x^3 - 9)

D. S(x) = (x^4 + |x - 4|)/(x^4 - 2x)
Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
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Determine if each function is even, odd or neither.
A. F(x) = (x)^(1/3) + |x|^2
B. G(x) = (1/x) - (x)^(1/4)
C. H(x) = [(x)^(1/2) + 12x]/(x^3 - 9)
D. S(x) = (x^4 + |x - 4|)/(x^4 - 2x)
~~~~~~~~~~~~~~~~~~~~~~


                I will answer  (B),  (C)  and  (D). 


(B)  In (B),  (x)^(1/4)  is defined only for  x >= 0.

     Therefore, function G(x) is defined only for  x >= 0.

     Therefore, the conception of even and/or odd function is inapplicable for G(x).

     Therefore, the answer for (B) is "neither".



(C)  In (C),  (x)^(1/2)  is defined only for  x >= 0.

     Therefore, function H(x) is defined only for  x >= 0.

     Therefore, the conception of even and/or odd function is inapplicable for H(x).

     Therefore, the answer for (C) is "neither".



(D)  In (D), calculate  S(x) at two values of x: x= 1 and x= -1.


     At x= 1,  S(1)  =  =  =  = -4.


     At x= -1, S(-1) =  =  =  = 2.


     So, neither  S(1) = S(-1)  nor  S(1) = -S(-1).  Thus we conclude that function S(x) is neither even nor odd.

Parts  (B),  (C)  and  (D)  are solved and answered,  with explanations.



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